Can Diplomacy be useful in flashpoints

If you want to make sure you got all the datacrons on a specific planet, look at the Codex entry for that planet and then click on the magnifying glass. It shows your progress on that planet, including how many of the datacrons you have:

As for the rewards from datacrons, it seems it's only stats boosts and matrix shards, but I can't say that for certain.

It looks like you've just been unlucky.

There is a group roll and the player who wins the roll says the dialogue option they chose. Everyone hears that player’s choice and the deal with the consequences of that choice.

This can lead to some interesting conversation dynamics if the leader is in the minority.

One important detail to note is that Light side and Dark side points are not awarded to the group for the choice depicted, but for each player individually according to the choice they made individually.

Source: Interview with developers

This matches what the Developers said when they walked through one of the first flashpoints - The Esseles.

Finally, the 1.1 patch notes allude that the game tries to "normalize" conversation rolls to make sure who "wins" each roll is approximately equal.

Players who spectated conversations no longer unleash an initial massive critical social roll in their next multiplayer conversation.

The above quote would seem to indicate that not getting to speak in one social roll gives a boost in your next social roll, resetting when you finally get a chance to speak.